tan^2 theta sec^2 theta- sec^2 theta + 1= tan^4 theta?

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tan^2 theta sec^2 theta- sec^2 theta + 1= tan^4 theta?

2007-08-04 18:31:03 · 1 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

1 answers

Prove the identity.

(tan²θ)(sec²θ) - sec²θ + 1 = tan^4 θ

Let's start with the left hand side.

Left Hand Side = (tan²θ)(sec²θ) - sec²θ + 1

= (tan²θ)(sec²θ) - (sec²θ - 1)

= (tan²θ)(sec²θ) - tan²θ = (tan²θ)(sec²θ - 1)

= (tan²θ)(tan²θ) = tan^4θ = Right Hand Side

2007-08-04 18:37:29 · answer #1 · answered by Northstar 7 · 0⤊ 0⤋